Roots of the equation will be

(-p+(p^2-32)^0.5)/2 & (-p-(p^2-32)^0.5)/2

difference between the roots

= - (p/2) + (p/2) + ((p^2-32)^0.5)/2) + ((p^2-32)^0.5)/2) = 2

= ((p^2-32)^0.5) = 2

= p^2 -32 = 4

=> p = **6**

So to cross-check the roots of the equation x^2 + 6x + 8 = 0 are x = -2 & -4. & since -2 - (-4) = 2, p=6 holds good.